The invention relates to a noise damping device of the general type described by the preamble to the main claim. It has already been proposed to dispose a diaphragm inside the housing of a fuel supply pump for the purpose of noise damping, with this diaphragm temporarily yielding in the case of pressure fluctuations and thereby effecting damping. A device of this kind, however, is no longer freely accessible after being mounted, so that if there is later damage, it may be necessary to open the supply pump rather violently for repair purposes. The occurrence of pressure fluctuations and thus noise buildup, in the case of fluid supplied by means of a fluid pump, is caused by the fact that this pump is embodied as a positive-displacement pump. Such pumps aspirate the medium to be supplied, compress it and expel it once again, with this procedure being cyclically repeated in rapid succession. In the case of a roller piston pump, which is frequently used as a positive-displacement pump for supplying fuel, the aspiration, compression and expulsion of the medium recurs as frequently per pump rotation as there are discrete chamber volumes available; that is, in a five-celled roller piston pump, it recurs five times per pump rotation. Each of these pumping procedures is associated with a brief drop in the suction underpressure and an increase in the supply pressure, the frequency of the pressure fluctuations thus occurring being determined by the pump rpm. Thus in various motor vehicles (if the fluid pumps to be damped are fuel supply pumps) the result can sometimes be an annoying buildup of noise in the passenger area of the vehicle. These noises are caused by the pressure fluctuations in the fuel supply system (which in turn are caused by the mode of operation of the pump system, as described above) as they travel through the lines and the chassis of the vehicle and spread out as sound waves in the air. A reduction of such pressure fluctuations at their source is hardly possible. Accordingly, the present invention is directed to reducing or entirely eliminating disturbing noises.